TB-LMTO-ASA method

Given the self-consistent density-functional calculation, let us now visualize the electronic structure of CaO in real space. Because the rock-salt structure is very regular, even a simpler DFT calculation (in terms of atomic potentials) will now suffice, and we therefore recalculate the electronic structure by means of the, much faster, TB-LMTO-ASA method. Since we also know the experimental lattice parameter a with absolute certainty, the less accurate LDA functional will perform nicely for that a. Figure 3.2 shows the theoretical electron density p(r) in the (100) plane, with the Ca atoms in the corners/center and the O atoms lying inbetween. 

In addition, let us quantum-chemically analyze the electronic structure of this simple material in terms of chemical bonding. This is very easy to do because the above-mentioned TB-LMTO-ASA method operates with an extremely short-ranged basis set, such that electron and energy-partitionings are straightforward. Figure 3.3 shows the results, namely the band structure, the density-of-states, and the crystal orbital Hamilton population analysis. 

The question of alternative structure can be answered by electronic-structure theory, and it turns out that a quantitative answer is slightly more complicated because different magnetic properties are calculated for the [NaCl] and [ZnS] types. Nonetheless, non-spin-polarized band-structure calculations are quite sufficient to supply us with a correct qualitative picture. This has been derived using the TB-LMTO-ASA method and the LDA functional, and they give the correct lattice parameters with lowest energies for both structure types [267], just as for the case of CaO. 

Second, using the fully relativistic version of the TB-LMTO-CPA method within the atomic sphere approximation (ASA) we have calculated the total energies for random alloys AiBi i at five concentrations, x — 0,0.25,0.5,0.75 and 1, and using the CW method modified for disordered alloys we have determined five interaction parameters Eq, D,V,T, and Q as before (superscript RA). Finally, the electronic structure of random alloys calculated by the TB-LMTO-CPA method served as an input of the GPM from which the pair interactions v(c) (superscript GPM) were determined. In order to eliminate the charge transfer effects in these calculations, the atomic radii were adjusted in such a way that atoms were charge neutral while preserving the total volume of the alloy. The quantity (c) used for comparisons is a sum of properly... 

Andersen, O. K. Jepsen, O. et al. The Stuttgart TB-LMTO-ASA-47 Program, MPI fiir Feukorperforschung Stuttgart, 1998. (b) Skriver. H. L. The LMTO Method. Springer Berlin. 1984. 

Within density-functional theory, a linear combination of overlapping non-orthogonal orbitals from first principles may be utilized to arrive at at full-potential local orbital (FPLO) method [213], and this k-dependent LCAO approach comes close to full-potential APW-based methods (see Sections 2.15.3 and 2.15.4) in terms of numerical accuracy, although FPLO is much faster simply because of the locality of the basis set. Even faster, due to a strongly simplified potential, is a parameter-free (density-functional) tight-binding method called TB-LMTO-ASA, derived through localization of a delocalized basis set (see Section 2.15.4). 

The electronic structure is determined using the ab initio all-electron scalar-relativistic tight-binding linecir muffin-tin orbital (TB-LMTO) method in the atomic-sphere approximation (ASA). The nnderlying lattice, zincblende structure, refers to an fee Bravais lattice with a basis which contains a cation site (at a(0,0,0)), an anion site (at o(j,, )), and two interstitial sites occupied by empty spheres (at a(, 5, h) and a(, , )) which in turn are necessary for a correct description of open lattices . ... 

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